How many hemispheres with a radius of 3 cm can be produced by melting down a hemisphere with a radius of 12 cm?

Correct option is B

​Given :

Radius of large hemisphere = 12 cm

Radius of small hemisphere = 3 cm

Volume is conserved when melting.

Formula Used :

Volume of a hemisphere:
V =$$\frac{2}{3}\pi r^3$$​​
Solution :

Volume of the large hemisphere

​$$V_L = \frac{2}{3}\pi (12)^3$$​​
= $$\frac{2}{3}\pi \times 1728$$​​
= 115$$2\pi$$​​

Volume of one small hemisphere

​$$V_S = \frac{2}{3}\pi (3)^3$$​​
​$$= \frac{2}{3}\pi \times 27$$​​
= 18$$\pi$$​​

Number of small hemispheres

$$\text{Number} = \frac{V_L}{V_S} \\ \ \\= \frac{1152\pi}{18\pi}\\ \ \\= 64$$​​